Positivity Results for spaces of rational curves
| Autor: | Beheshti, Roya, Riedl, Eric |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Alg. Number Th. 14 (2020) 485-501 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2020.14.485 |
| Popis: | Let $X$ be a very general hypersurface of degree $d$ in $\mathbb{P}^n$. We investigate positivity properties of the spaces $R_e(X)$ of degree $e$ rational curves in $X$. We show that for small $e$, $R_e(X)$ has no rational curves meeting the locus of smooth embedded curves. We show that for $n \leq d$, there are no rational curves in the locus $Y \subset X$ swept out by lines. And we exhibit differential forms on a smooth compactification of $R_e(X)$ for every $e$ and $n-2 \geq d \geq \frac{n+1}{2}$. Comment: revised version |
| Databáze: | arXiv |
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